Geometry of a generalized uncertainty-inspired spacetime

Abstract

We examine the geometry of a generalized uncertainty-inspired quantum black hole. The diagonal line element is not $t$-$r$ symmetric, i.e. $g_{00}\ne -1/g_{11}$, which leads to an interesting approach to resolving the classical curvature singularity. In this paper, we show, in Schwarzschild coordinates, the $r=0$ coordinate location is a null surface which is not a transition surface or leads to a black bounce. We find the expansion of null geodesic congruences in the interior turn around then vanishes at $r=0$, and the energy conditions are predominately violated indicating a repulsive gravitational core. In addition, we show that the line element admits a wormhole solution which is not traversable, and the black hole at its vanishing horizon radius could be interpreted as a remnant.

31 pages, 10 figures; version accepted by PRD